What beginner-friendly machine learning method should I use to make teams for my pickup ultimate frisbee club fairly balanced?
What you have on your hands is an attribution problem (and that’s a good keyword to help in your Googling). Two common approaches are computing Shapley values or a Markov chain. 

In your case, I think Shapley values would be a good approach. To over-simplify, this approach attempts to first determine the total “surplus” of value created by different combinations of players, and then estimate how much was due to each player in the combination. Also under consideration are constrained combinatorial effects: e.g. having two great goalies doesn’t add much over one great goalie since they can’t play at the same time. 

Depending on how hands-on you want to be you could implement yourself or find existing libraries by Googling e.g. “Shapley values python”.